1

Project FP7-604416 DEEPEN

D24 Initial tight-binding and EMA parameter database

Due delivery date January 2016

Actual delivery date March 2016

Work package WP2

Deliverable Lead Partner Tyndall-UCC

Contributing partners ETHZ TIBER

Nature Report Version V10

Dissemination Level

PU Public

PP Restricted to other programme participants (including the Commission Services)

RE Restricted to a group specified by the consortium (including the Commission Services)

CO Confidential only for members of the consortium (including the Commission Services)

Executive Summary

This document reports on the delivery of an initial database for ab-initio computed band structure structural mechanical physical and piezoelectric parameters for both unstrained and strained III-V binaries and ternary alloys as specified in Task 21 and obtained in Tasks 22 23 24 and 25 The set of calculated material parameters is integrated into the multi-scale framework of WP4 which provides parametric coupling between ab-initio atomistic simulation tools and drift-diffusion simulators (Sentaurus-Device TiberCAD) The band structures and material parameters calculated within Task 22 23 24 and 25 serve as input parameters for kp and tight-binding model-based quantum transport solvers The data reported here provide a database of band structure and material parameters for channel materials such as strained InGaAs ternary alloys or ternary wurtzite (InGaAl)N alloys

2

Contents 1 Introduction 3

2 Basic structure parameters for unstrained InxGa1-xAs alloys 3

21 Lattice parameters 3

22 Band gap and higher energies of conduction band valleys 4

23 Electron and hole effective masses 4

3 Deformation potentials for band parameters of InxGa1-xAs alloys 5

4 Mechanical properties of InxGa1-xAs alloys 6

5 Ab-initio derived tight-binding parameters as used in OMEN 7

6 Band offsets 9

7 Temperature and doping dependencies 9

8 Mechanical properties of III-Nitrides 9

81 Wurtzite InN GaN and AlN 9

82 Zincblende InN GaN and AlN 10

9 Band offsets band gap and edge bowing parameters for III-Nitrides 10

10 Ab-inito derived tight-binding parameters for III-Nitrides 11

11 kp parameters for III-N materials 12

12 Piezoelectric coefficients for III-V materials 12

121 Wurtzite InN GaN and AlN 12

122 Zincblende III-V materials 13

13 Conclusions 13

3

1 Introduction We summarize the data obtained with first-principles calculations for band structure and material parameters of unstrained and strained InxGa1-xAs compounds as well as for III-Nitride materials This report contains a detailed description of deliverable D24 (initial database of III-V semiconductor material parameters) in relation to Tasks 22 and 23 (parameter calculations) and Tasks 24 and 25 (parameter extraction)

First we report band structure and structural data in a tabulated form for InxGa1-xAs compounds with x = 0 025 05 053 075 and 10 In particular lattice constants band gap and higher energies of the conduction band valleys are given together with the corresponding compositional bowing parameters in the tables Effective masses for heavy light and split-off holes as well as electron effective masses at the Γ X and L conduction band valleys are summarized as well These data provide input for a kp model and drift-diffusion model and we used them to obtain tight-binding parameters as required for a tight-binding model-based quantum transport solver (OMEN)

Second we have tabulated deformation potentials for band structure parameters for the InxGa1-

xAs ternary alloys with x = 0 025 05 053 075 and 10 for various strain configurations as required for a kp model and a tight-binding model-based quantum transport solver (OMEN) The corresponding compositional bowing parameters of the deformation potentials are given as well

Thirdly we have provided a set of parameters that characterize mechanical properties of the InxGa1-xAs ternary alloy with relevant alloy compositions such as x = 0 05 053 and 10 In particular the elasticity tensor bulk modulus and Poisson ratios as well as their compositional bowing parameters are tabulated

Note that knowing the compositional bowing parameter bw for a given physical quantity Q allows calculating the physical quantity value Q(x) for any ternary alloy composition x using the following formula Q(x) = x Q(1) + (1 - x) Q(0) - bw x (1 ndash x) where the physical quantity values Q(0) and Q(1) correspond to the binary materials under consideration

Similar results have been derived for wurtzite and zinc blende III-nitride materials including also piezoelectric coefficients and multi-band kp parameters

The ab-initio band structure and other physical parameters of the semiconductor compounds obtained in Tasks 22 and 23 and extracted in Tasks 24 and 25 provide an initial database of tight-binding and effective mass approximation (EMA) parameters The programming scripts for visualizing the band structure and extracting physical parameters such as energies and effective masses have been deposited at the DEEPEN website

2 Basic structure parameters for unstrained InxGa1-xAs alloys

21 Lattice parameters

In Table 1 we report the hybrid (HSE06) functional calculated lattice constant values of InxGa1-

xAs alloys with x=0 025 050 053 075 and 10 For the sake of comparison the experimental and LDA-calculated values of these lattice parameters are also given in the table

4

bw (Aring) GaAs In025Ga075As In050Ga050As In053Ga047As In075Ga025As InAs

a (Aring) ~0 5677 5784 5891 5903 5997 6104

aLDA (Aring) ~0 5611 5716 5822 5834 5927 6032

aexp (Aring) 0 K ~0 5648 5750 5851 5863 5953 6054

aexp (Aring)300K ~0 5654 5755 5856 5868 5957 6058

Table 1 HSE06 (LDA)-calculated lattice constants a (aLDA) of InAs GaAs and InxGa1-xAs with x=025 050 053 and 075 bw is the bowing parameter The experimental lattice parameters aexp at T=0 and

300 K are also included in the table

22 Band gap and higher energies of conduction band valleys

In Table 2 we give the most important band structure parameters of GaAs InAs and InGaAs compounds (i) the band gap energy (Eg) defined as the difference between the top valence band and the bottom of the conduction band at the Γ-point (ii) two higher conduction band energies (EX and EL) at the X and L-valleys defined with respect to the top of the valence band and (iii) the spin-orbit splitting (Δso) between the top and split-off valence bands The compositional dependence of all the band structure parameters is characterized with the compositional bowing parameter bw given in Table 2

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

Egap(eV) 055 132 098 072 069 052 039

EL (eV) 031 165 156 151 151 150 153

EX (eV) - 191 195 196 195 197 200

EX (eV) 0105 195 195 196 195 197 200

Δso (eV) 00 0360 0365 0370 0370 0375 0380

Table 2 Band gap spin-orbit splitting of valence bands at the Γ-point and higher energies of conduction bands at the Γ X and L valleys for the InxGa1-xAs alloy with x=00 025 050 053 075 and 10 (spin-orbit coupling included) These energies are calculated with a hybrid functional approach The bowing parameter is obtained by hybrid (HSE06) functional calculations without spin-orbit coupling included Note that E

X is

the conduction band energy exactly at the X-point ie not at the X valley minimum EX =EX for xgt025

23 Electron and hole effective masses

In Table 3 we report the hybrid (HSE06) functional-calculated electron effective mass and the related non-parabolicity parameter of the conduction band for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloys The heavy light and split-off hole effective masses for different band valleys and crystallographic directions are also reported in Table 3 All the effective mass parameters were calculated taking into account the spin-orbit coupling

5

GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

me 0062 0053 0043 0042 0034 0024

α (eV-1) 0802 122 163 168 205 246

mhh [001] 0313 0321 0330 0331 0338 0346

[111] 0772 0738 0704 0700 0670 0636

[110] 0565 0555 0546 0544 0536 0526

mlh [001] 0078 0066 0054 0052 0041 0029

[111] 0070 0060 0049 0048 0039 0028

[110] 0070 0060 0049 0048 0039 0028

mso 0160 0147 0133 0131 0120 0106

mLl 162 169 177 177 184 191

mLt 0109 0110 0111 0112 0113 0114

mXl 110 125 140 142 155 170

mXt 0210 0217 0224 0224 0230 0237

Table 3 Effective masses of heavy (mhh) light (mlh) and split-off (mso) holes and electron effective masses at the Γ X and L points for the InxGa1-xAs alloy with x=00 025 050 053 075 10 (spin-orbit coupling is included) Effective masses of the ternary alloys are calculated according to Vegardrsquos law in combination with hybrid functional calculations for the effective masses of binary alloys (GaAs InAs) α is the non-parabolicity parameter of the conduction band

3 Deformation potentials for band parameters of InxGa1-xAs alloys In the linear approximation any deformation of the InxGa1-xAs alloy structure can be represented as a combination of the hydrostatic and shear deformations To describe the hydrostatic deformation effect on the band gap we report a hydrostatic deformation potential ag=aΓ in Table 4 Besides the hydrostatic strain effect on the conduction and valence bands at the Γ-point the hydrostatic deformation also shifts the higher conduction band energies at the X and L-valleys with respect to the top of the valence bands at the Γ-point The corresponding hydrostatic deformation potentials aX and aL are reported in Table 4 together with the corresponding compositional bowing parameters bw

The shear deformations cause both conduction and valence band splitting quantified by the corresponding shear deformation potentials ΞuX ΞuL b and d that are given in Table 4 and 5 according to kmiddotp model conventions The deformation potential values can then be directly used within the framework of a kmiddotp model and tight-binding model

We would like to notice that the conduction band hydrostatic deformation potentials aΓ aX and aL in Table 5 can be expressed as aΓ = ΞdΓ - aV and aC = ΞdC + ΞuC3 - aV where C = L or X and ΞdΓ ΞdC and ΞuC are the deformation potentials as defined by Herring and Vogt [Phys Rev 101 944 (1956)] and aV is the hydrostatic deformation potential for the average of three top valence bands at the Γ-point The electronic states at the Γ and L (Γ and X) valleys of the face-centered cubic Brillouin zone (BZ) of InxGa1-xAs alloys are not affected by the shear strain type I (type II) as discussed by Khomyakov et al [Appl Phys Lett 107 062104 (2015)] being protected by symmetry ie ΞuΓ = 0 The three X (four L) valleys are split by the shear strain type I (type II) into three singlets (doublets) with a shift of ΔEX = 0 and ΔEX = plusmnΞuX |ε| (ΔEL =plusmn2 ΞuC |ε|3) with respect to the averaged conduction band energy ε is the strain parameter

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

2

Contents 1 Introduction 3

2 Basic structure parameters for unstrained InxGa1-xAs alloys 3

21 Lattice parameters 3

22 Band gap and higher energies of conduction band valleys 4

23 Electron and hole effective masses 4

3 Deformation potentials for band parameters of InxGa1-xAs alloys 5

4 Mechanical properties of InxGa1-xAs alloys 6

5 Ab-initio derived tight-binding parameters as used in OMEN 7

6 Band offsets 9

7 Temperature and doping dependencies 9

8 Mechanical properties of III-Nitrides 9

81 Wurtzite InN GaN and AlN 9

82 Zincblende InN GaN and AlN 10

9 Band offsets band gap and edge bowing parameters for III-Nitrides 10

10 Ab-inito derived tight-binding parameters for III-Nitrides 11

11 kp parameters for III-N materials 12

12 Piezoelectric coefficients for III-V materials 12

121 Wurtzite InN GaN and AlN 12

122 Zincblende III-V materials 13

13 Conclusions 13

3

1 Introduction We summarize the data obtained with first-principles calculations for band structure and material parameters of unstrained and strained InxGa1-xAs compounds as well as for III-Nitride materials This report contains a detailed description of deliverable D24 (initial database of III-V semiconductor material parameters) in relation to Tasks 22 and 23 (parameter calculations) and Tasks 24 and 25 (parameter extraction)

First we report band structure and structural data in a tabulated form for InxGa1-xAs compounds with x = 0 025 05 053 075 and 10 In particular lattice constants band gap and higher energies of the conduction band valleys are given together with the corresponding compositional bowing parameters in the tables Effective masses for heavy light and split-off holes as well as electron effective masses at the Γ X and L conduction band valleys are summarized as well These data provide input for a kp model and drift-diffusion model and we used them to obtain tight-binding parameters as required for a tight-binding model-based quantum transport solver (OMEN)

Second we have tabulated deformation potentials for band structure parameters for the InxGa1-

xAs ternary alloys with x = 0 025 05 053 075 and 10 for various strain configurations as required for a kp model and a tight-binding model-based quantum transport solver (OMEN) The corresponding compositional bowing parameters of the deformation potentials are given as well

Thirdly we have provided a set of parameters that characterize mechanical properties of the InxGa1-xAs ternary alloy with relevant alloy compositions such as x = 0 05 053 and 10 In particular the elasticity tensor bulk modulus and Poisson ratios as well as their compositional bowing parameters are tabulated

Note that knowing the compositional bowing parameter bw for a given physical quantity Q allows calculating the physical quantity value Q(x) for any ternary alloy composition x using the following formula Q(x) = x Q(1) + (1 - x) Q(0) - bw x (1 ndash x) where the physical quantity values Q(0) and Q(1) correspond to the binary materials under consideration

Similar results have been derived for wurtzite and zinc blende III-nitride materials including also piezoelectric coefficients and multi-band kp parameters

The ab-initio band structure and other physical parameters of the semiconductor compounds obtained in Tasks 22 and 23 and extracted in Tasks 24 and 25 provide an initial database of tight-binding and effective mass approximation (EMA) parameters The programming scripts for visualizing the band structure and extracting physical parameters such as energies and effective masses have been deposited at the DEEPEN website

2 Basic structure parameters for unstrained InxGa1-xAs alloys

21 Lattice parameters

In Table 1 we report the hybrid (HSE06) functional calculated lattice constant values of InxGa1-

xAs alloys with x=0 025 050 053 075 and 10 For the sake of comparison the experimental and LDA-calculated values of these lattice parameters are also given in the table

4

bw (Aring) GaAs In025Ga075As In050Ga050As In053Ga047As In075Ga025As InAs

a (Aring) ~0 5677 5784 5891 5903 5997 6104

aLDA (Aring) ~0 5611 5716 5822 5834 5927 6032

aexp (Aring) 0 K ~0 5648 5750 5851 5863 5953 6054

aexp (Aring)300K ~0 5654 5755 5856 5868 5957 6058

Table 1 HSE06 (LDA)-calculated lattice constants a (aLDA) of InAs GaAs and InxGa1-xAs with x=025 050 053 and 075 bw is the bowing parameter The experimental lattice parameters aexp at T=0 and

300 K are also included in the table

22 Band gap and higher energies of conduction band valleys

In Table 2 we give the most important band structure parameters of GaAs InAs and InGaAs compounds (i) the band gap energy (Eg) defined as the difference between the top valence band and the bottom of the conduction band at the Γ-point (ii) two higher conduction band energies (EX and EL) at the X and L-valleys defined with respect to the top of the valence band and (iii) the spin-orbit splitting (Δso) between the top and split-off valence bands The compositional dependence of all the band structure parameters is characterized with the compositional bowing parameter bw given in Table 2

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

Egap(eV) 055 132 098 072 069 052 039

EL (eV) 031 165 156 151 151 150 153

EX (eV) - 191 195 196 195 197 200

EX (eV) 0105 195 195 196 195 197 200

Δso (eV) 00 0360 0365 0370 0370 0375 0380

Table 2 Band gap spin-orbit splitting of valence bands at the Γ-point and higher energies of conduction bands at the Γ X and L valleys for the InxGa1-xAs alloy with x=00 025 050 053 075 and 10 (spin-orbit coupling included) These energies are calculated with a hybrid functional approach The bowing parameter is obtained by hybrid (HSE06) functional calculations without spin-orbit coupling included Note that E

X is

the conduction band energy exactly at the X-point ie not at the X valley minimum EX =EX for xgt025

23 Electron and hole effective masses

In Table 3 we report the hybrid (HSE06) functional-calculated electron effective mass and the related non-parabolicity parameter of the conduction band for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloys The heavy light and split-off hole effective masses for different band valleys and crystallographic directions are also reported in Table 3 All the effective mass parameters were calculated taking into account the spin-orbit coupling

5

GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

me 0062 0053 0043 0042 0034 0024

α (eV-1) 0802 122 163 168 205 246

mhh [001] 0313 0321 0330 0331 0338 0346

[111] 0772 0738 0704 0700 0670 0636

[110] 0565 0555 0546 0544 0536 0526

mlh [001] 0078 0066 0054 0052 0041 0029

[111] 0070 0060 0049 0048 0039 0028

[110] 0070 0060 0049 0048 0039 0028

mso 0160 0147 0133 0131 0120 0106

mLl 162 169 177 177 184 191

mLt 0109 0110 0111 0112 0113 0114

mXl 110 125 140 142 155 170

mXt 0210 0217 0224 0224 0230 0237

Table 3 Effective masses of heavy (mhh) light (mlh) and split-off (mso) holes and electron effective masses at the Γ X and L points for the InxGa1-xAs alloy with x=00 025 050 053 075 10 (spin-orbit coupling is included) Effective masses of the ternary alloys are calculated according to Vegardrsquos law in combination with hybrid functional calculations for the effective masses of binary alloys (GaAs InAs) α is the non-parabolicity parameter of the conduction band

3 Deformation potentials for band parameters of InxGa1-xAs alloys In the linear approximation any deformation of the InxGa1-xAs alloy structure can be represented as a combination of the hydrostatic and shear deformations To describe the hydrostatic deformation effect on the band gap we report a hydrostatic deformation potential ag=aΓ in Table 4 Besides the hydrostatic strain effect on the conduction and valence bands at the Γ-point the hydrostatic deformation also shifts the higher conduction band energies at the X and L-valleys with respect to the top of the valence bands at the Γ-point The corresponding hydrostatic deformation potentials aX and aL are reported in Table 4 together with the corresponding compositional bowing parameters bw

The shear deformations cause both conduction and valence band splitting quantified by the corresponding shear deformation potentials ΞuX ΞuL b and d that are given in Table 4 and 5 according to kmiddotp model conventions The deformation potential values can then be directly used within the framework of a kmiddotp model and tight-binding model

We would like to notice that the conduction band hydrostatic deformation potentials aΓ aX and aL in Table 5 can be expressed as aΓ = ΞdΓ - aV and aC = ΞdC + ΞuC3 - aV where C = L or X and ΞdΓ ΞdC and ΞuC are the deformation potentials as defined by Herring and Vogt [Phys Rev 101 944 (1956)] and aV is the hydrostatic deformation potential for the average of three top valence bands at the Γ-point The electronic states at the Γ and L (Γ and X) valleys of the face-centered cubic Brillouin zone (BZ) of InxGa1-xAs alloys are not affected by the shear strain type I (type II) as discussed by Khomyakov et al [Appl Phys Lett 107 062104 (2015)] being protected by symmetry ie ΞuΓ = 0 The three X (four L) valleys are split by the shear strain type I (type II) into three singlets (doublets) with a shift of ΔEX = 0 and ΔEX = plusmnΞuX |ε| (ΔEL =plusmn2 ΞuC |ε|3) with respect to the averaged conduction band energy ε is the strain parameter

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

3

1 Introduction We summarize the data obtained with first-principles calculations for band structure and material parameters of unstrained and strained InxGa1-xAs compounds as well as for III-Nitride materials This report contains a detailed description of deliverable D24 (initial database of III-V semiconductor material parameters) in relation to Tasks 22 and 23 (parameter calculations) and Tasks 24 and 25 (parameter extraction)

First we report band structure and structural data in a tabulated form for InxGa1-xAs compounds with x = 0 025 05 053 075 and 10 In particular lattice constants band gap and higher energies of the conduction band valleys are given together with the corresponding compositional bowing parameters in the tables Effective masses for heavy light and split-off holes as well as electron effective masses at the Γ X and L conduction band valleys are summarized as well These data provide input for a kp model and drift-diffusion model and we used them to obtain tight-binding parameters as required for a tight-binding model-based quantum transport solver (OMEN)

Second we have tabulated deformation potentials for band structure parameters for the InxGa1-

xAs ternary alloys with x = 0 025 05 053 075 and 10 for various strain configurations as required for a kp model and a tight-binding model-based quantum transport solver (OMEN) The corresponding compositional bowing parameters of the deformation potentials are given as well

Thirdly we have provided a set of parameters that characterize mechanical properties of the InxGa1-xAs ternary alloy with relevant alloy compositions such as x = 0 05 053 and 10 In particular the elasticity tensor bulk modulus and Poisson ratios as well as their compositional bowing parameters are tabulated

Note that knowing the compositional bowing parameter bw for a given physical quantity Q allows calculating the physical quantity value Q(x) for any ternary alloy composition x using the following formula Q(x) = x Q(1) + (1 - x) Q(0) - bw x (1 ndash x) where the physical quantity values Q(0) and Q(1) correspond to the binary materials under consideration

Similar results have been derived for wurtzite and zinc blende III-nitride materials including also piezoelectric coefficients and multi-band kp parameters

The ab-initio band structure and other physical parameters of the semiconductor compounds obtained in Tasks 22 and 23 and extracted in Tasks 24 and 25 provide an initial database of tight-binding and effective mass approximation (EMA) parameters The programming scripts for visualizing the band structure and extracting physical parameters such as energies and effective masses have been deposited at the DEEPEN website

2 Basic structure parameters for unstrained InxGa1-xAs alloys

21 Lattice parameters

In Table 1 we report the hybrid (HSE06) functional calculated lattice constant values of InxGa1-

xAs alloys with x=0 025 050 053 075 and 10 For the sake of comparison the experimental and LDA-calculated values of these lattice parameters are also given in the table

4

bw (Aring) GaAs In025Ga075As In050Ga050As In053Ga047As In075Ga025As InAs

a (Aring) ~0 5677 5784 5891 5903 5997 6104

aLDA (Aring) ~0 5611 5716 5822 5834 5927 6032

aexp (Aring) 0 K ~0 5648 5750 5851 5863 5953 6054

aexp (Aring)300K ~0 5654 5755 5856 5868 5957 6058

Table 1 HSE06 (LDA)-calculated lattice constants a (aLDA) of InAs GaAs and InxGa1-xAs with x=025 050 053 and 075 bw is the bowing parameter The experimental lattice parameters aexp at T=0 and

300 K are also included in the table

22 Band gap and higher energies of conduction band valleys

In Table 2 we give the most important band structure parameters of GaAs InAs and InGaAs compounds (i) the band gap energy (Eg) defined as the difference between the top valence band and the bottom of the conduction band at the Γ-point (ii) two higher conduction band energies (EX and EL) at the X and L-valleys defined with respect to the top of the valence band and (iii) the spin-orbit splitting (Δso) between the top and split-off valence bands The compositional dependence of all the band structure parameters is characterized with the compositional bowing parameter bw given in Table 2

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

Egap(eV) 055 132 098 072 069 052 039

EL (eV) 031 165 156 151 151 150 153

EX (eV) - 191 195 196 195 197 200

EX (eV) 0105 195 195 196 195 197 200

Δso (eV) 00 0360 0365 0370 0370 0375 0380

Table 2 Band gap spin-orbit splitting of valence bands at the Γ-point and higher energies of conduction bands at the Γ X and L valleys for the InxGa1-xAs alloy with x=00 025 050 053 075 and 10 (spin-orbit coupling included) These energies are calculated with a hybrid functional approach The bowing parameter is obtained by hybrid (HSE06) functional calculations without spin-orbit coupling included Note that E

X is

the conduction band energy exactly at the X-point ie not at the X valley minimum EX =EX for xgt025

23 Electron and hole effective masses

In Table 3 we report the hybrid (HSE06) functional-calculated electron effective mass and the related non-parabolicity parameter of the conduction band for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloys The heavy light and split-off hole effective masses for different band valleys and crystallographic directions are also reported in Table 3 All the effective mass parameters were calculated taking into account the spin-orbit coupling

5

GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

me 0062 0053 0043 0042 0034 0024

α (eV-1) 0802 122 163 168 205 246

mhh [001] 0313 0321 0330 0331 0338 0346

[111] 0772 0738 0704 0700 0670 0636

[110] 0565 0555 0546 0544 0536 0526

mlh [001] 0078 0066 0054 0052 0041 0029

[111] 0070 0060 0049 0048 0039 0028

[110] 0070 0060 0049 0048 0039 0028

mso 0160 0147 0133 0131 0120 0106

mLl 162 169 177 177 184 191

mLt 0109 0110 0111 0112 0113 0114

mXl 110 125 140 142 155 170

mXt 0210 0217 0224 0224 0230 0237

Table 3 Effective masses of heavy (mhh) light (mlh) and split-off (mso) holes and electron effective masses at the Γ X and L points for the InxGa1-xAs alloy with x=00 025 050 053 075 10 (spin-orbit coupling is included) Effective masses of the ternary alloys are calculated according to Vegardrsquos law in combination with hybrid functional calculations for the effective masses of binary alloys (GaAs InAs) α is the non-parabolicity parameter of the conduction band

3 Deformation potentials for band parameters of InxGa1-xAs alloys In the linear approximation any deformation of the InxGa1-xAs alloy structure can be represented as a combination of the hydrostatic and shear deformations To describe the hydrostatic deformation effect on the band gap we report a hydrostatic deformation potential ag=aΓ in Table 4 Besides the hydrostatic strain effect on the conduction and valence bands at the Γ-point the hydrostatic deformation also shifts the higher conduction band energies at the X and L-valleys with respect to the top of the valence bands at the Γ-point The corresponding hydrostatic deformation potentials aX and aL are reported in Table 4 together with the corresponding compositional bowing parameters bw

The shear deformations cause both conduction and valence band splitting quantified by the corresponding shear deformation potentials ΞuX ΞuL b and d that are given in Table 4 and 5 according to kmiddotp model conventions The deformation potential values can then be directly used within the framework of a kmiddotp model and tight-binding model

We would like to notice that the conduction band hydrostatic deformation potentials aΓ aX and aL in Table 5 can be expressed as aΓ = ΞdΓ - aV and aC = ΞdC + ΞuC3 - aV where C = L or X and ΞdΓ ΞdC and ΞuC are the deformation potentials as defined by Herring and Vogt [Phys Rev 101 944 (1956)] and aV is the hydrostatic deformation potential for the average of three top valence bands at the Γ-point The electronic states at the Γ and L (Γ and X) valleys of the face-centered cubic Brillouin zone (BZ) of InxGa1-xAs alloys are not affected by the shear strain type I (type II) as discussed by Khomyakov et al [Appl Phys Lett 107 062104 (2015)] being protected by symmetry ie ΞuΓ = 0 The three X (four L) valleys are split by the shear strain type I (type II) into three singlets (doublets) with a shift of ΔEX = 0 and ΔEX = plusmnΞuX |ε| (ΔEL =plusmn2 ΞuC |ε|3) with respect to the averaged conduction band energy ε is the strain parameter

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

4

bw (Aring) GaAs In025Ga075As In050Ga050As In053Ga047As In075Ga025As InAs

a (Aring) ~0 5677 5784 5891 5903 5997 6104

aLDA (Aring) ~0 5611 5716 5822 5834 5927 6032

aexp (Aring) 0 K ~0 5648 5750 5851 5863 5953 6054

aexp (Aring)300K ~0 5654 5755 5856 5868 5957 6058

Table 1 HSE06 (LDA)-calculated lattice constants a (aLDA) of InAs GaAs and InxGa1-xAs with x=025 050 053 and 075 bw is the bowing parameter The experimental lattice parameters aexp at T=0 and

300 K are also included in the table

22 Band gap and higher energies of conduction band valleys

In Table 2 we give the most important band structure parameters of GaAs InAs and InGaAs compounds (i) the band gap energy (Eg) defined as the difference between the top valence band and the bottom of the conduction band at the Γ-point (ii) two higher conduction band energies (EX and EL) at the X and L-valleys defined with respect to the top of the valence band and (iii) the spin-orbit splitting (Δso) between the top and split-off valence bands The compositional dependence of all the band structure parameters is characterized with the compositional bowing parameter bw given in Table 2

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

Egap(eV) 055 132 098 072 069 052 039

EL (eV) 031 165 156 151 151 150 153

EX (eV) - 191 195 196 195 197 200

EX (eV) 0105 195 195 196 195 197 200

Δso (eV) 00 0360 0365 0370 0370 0375 0380

Table 2 Band gap spin-orbit splitting of valence bands at the Γ-point and higher energies of conduction bands at the Γ X and L valleys for the InxGa1-xAs alloy with x=00 025 050 053 075 and 10 (spin-orbit coupling included) These energies are calculated with a hybrid functional approach The bowing parameter is obtained by hybrid (HSE06) functional calculations without spin-orbit coupling included Note that E

X is

the conduction band energy exactly at the X-point ie not at the X valley minimum EX =EX for xgt025

23 Electron and hole effective masses

In Table 3 we report the hybrid (HSE06) functional-calculated electron effective mass and the related non-parabolicity parameter of the conduction band for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloys The heavy light and split-off hole effective masses for different band valleys and crystallographic directions are also reported in Table 3 All the effective mass parameters were calculated taking into account the spin-orbit coupling

5

GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

me 0062 0053 0043 0042 0034 0024

α (eV-1) 0802 122 163 168 205 246

mhh [001] 0313 0321 0330 0331 0338 0346

[111] 0772 0738 0704 0700 0670 0636

[110] 0565 0555 0546 0544 0536 0526

mlh [001] 0078 0066 0054 0052 0041 0029

[111] 0070 0060 0049 0048 0039 0028

[110] 0070 0060 0049 0048 0039 0028

mso 0160 0147 0133 0131 0120 0106

mLl 162 169 177 177 184 191

mLt 0109 0110 0111 0112 0113 0114

mXl 110 125 140 142 155 170

mXt 0210 0217 0224 0224 0230 0237

Table 3 Effective masses of heavy (mhh) light (mlh) and split-off (mso) holes and electron effective masses at the Γ X and L points for the InxGa1-xAs alloy with x=00 025 050 053 075 10 (spin-orbit coupling is included) Effective masses of the ternary alloys are calculated according to Vegardrsquos law in combination with hybrid functional calculations for the effective masses of binary alloys (GaAs InAs) α is the non-parabolicity parameter of the conduction band

3 Deformation potentials for band parameters of InxGa1-xAs alloys In the linear approximation any deformation of the InxGa1-xAs alloy structure can be represented as a combination of the hydrostatic and shear deformations To describe the hydrostatic deformation effect on the band gap we report a hydrostatic deformation potential ag=aΓ in Table 4 Besides the hydrostatic strain effect on the conduction and valence bands at the Γ-point the hydrostatic deformation also shifts the higher conduction band energies at the X and L-valleys with respect to the top of the valence bands at the Γ-point The corresponding hydrostatic deformation potentials aX and aL are reported in Table 4 together with the corresponding compositional bowing parameters bw

The shear deformations cause both conduction and valence band splitting quantified by the corresponding shear deformation potentials ΞuX ΞuL b and d that are given in Table 4 and 5 according to kmiddotp model conventions The deformation potential values can then be directly used within the framework of a kmiddotp model and tight-binding model

We would like to notice that the conduction band hydrostatic deformation potentials aΓ aX and aL in Table 5 can be expressed as aΓ = ΞdΓ - aV and aC = ΞdC + ΞuC3 - aV where C = L or X and ΞdΓ ΞdC and ΞuC are the deformation potentials as defined by Herring and Vogt [Phys Rev 101 944 (1956)] and aV is the hydrostatic deformation potential for the average of three top valence bands at the Γ-point The electronic states at the Γ and L (Γ and X) valleys of the face-centered cubic Brillouin zone (BZ) of InxGa1-xAs alloys are not affected by the shear strain type I (type II) as discussed by Khomyakov et al [Appl Phys Lett 107 062104 (2015)] being protected by symmetry ie ΞuΓ = 0 The three X (four L) valleys are split by the shear strain type I (type II) into three singlets (doublets) with a shift of ΔEX = 0 and ΔEX = plusmnΞuX |ε| (ΔEL =plusmn2 ΞuC |ε|3) with respect to the averaged conduction band energy ε is the strain parameter

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

5

GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

me 0062 0053 0043 0042 0034 0024

α (eV-1) 0802 122 163 168 205 246

mhh [001] 0313 0321 0330 0331 0338 0346

[111] 0772 0738 0704 0700 0670 0636

[110] 0565 0555 0546 0544 0536 0526

mlh [001] 0078 0066 0054 0052 0041 0029

[111] 0070 0060 0049 0048 0039 0028

[110] 0070 0060 0049 0048 0039 0028

mso 0160 0147 0133 0131 0120 0106

mLl 162 169 177 177 184 191

mLt 0109 0110 0111 0112 0113 0114

mXl 110 125 140 142 155 170

mXt 0210 0217 0224 0224 0230 0237

Table 3 Effective masses of heavy (mhh) light (mlh) and split-off (mso) holes and electron effective masses at the Γ X and L points for the InxGa1-xAs alloy with x=00 025 050 053 075 10 (spin-orbit coupling is included) Effective masses of the ternary alloys are calculated according to Vegardrsquos law in combination with hybrid functional calculations for the effective masses of binary alloys (GaAs InAs) α is the non-parabolicity parameter of the conduction band

3 Deformation potentials for band parameters of InxGa1-xAs alloys In the linear approximation any deformation of the InxGa1-xAs alloy structure can be represented as a combination of the hydrostatic and shear deformations To describe the hydrostatic deformation effect on the band gap we report a hydrostatic deformation potential ag=aΓ in Table 4 Besides the hydrostatic strain effect on the conduction and valence bands at the Γ-point the hydrostatic deformation also shifts the higher conduction band energies at the X and L-valleys with respect to the top of the valence bands at the Γ-point The corresponding hydrostatic deformation potentials aX and aL are reported in Table 4 together with the corresponding compositional bowing parameters bw

The shear deformations cause both conduction and valence band splitting quantified by the corresponding shear deformation potentials ΞuX ΞuL b and d that are given in Table 4 and 5 according to kmiddotp model conventions The deformation potential values can then be directly used within the framework of a kmiddotp model and tight-binding model

We would like to notice that the conduction band hydrostatic deformation potentials aΓ aX and aL in Table 5 can be expressed as aΓ = ΞdΓ - aV and aC = ΞdC + ΞuC3 - aV where C = L or X and ΞdΓ ΞdC and ΞuC are the deformation potentials as defined by Herring and Vogt [Phys Rev 101 944 (1956)] and aV is the hydrostatic deformation potential for the average of three top valence bands at the Γ-point The electronic states at the Γ and L (Γ and X) valleys of the face-centered cubic Brillouin zone (BZ) of InxGa1-xAs alloys are not affected by the shear strain type I (type II) as discussed by Khomyakov et al [Appl Phys Lett 107 062104 (2015)] being protected by symmetry ie ΞuΓ = 0 The three X (four L) valleys are split by the shear strain type I (type II) into three singlets (doublets) with a shift of ΔEX = 0 and ΔEX = plusmnΞuX |ε| (ΔEL =plusmn2 ΞuC |ε|3) with respect to the averaged conduction band energy ε is the strain parameter

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

6

bw(eV) GaAs In025Ga075As In05Ga05As In053Ga047As In075Ga025As InAs

aΓ (eV) -147 -854 -762 -689 -681 -634 -597

aL (eV) -083 -335 -303 -281 -279 -270 -269

aX (eV) - 139 161 150 150 145 145

aX (eV) +040 176 161 150 150 145 145

b (eV) -020 -201 -189 -180 -179 -173 -169

d (eV) -043 -433 -410 -392 -390 -379 -372

Table 4 The hydrostatic and shear deformation potentials aΓ aL aX aX b and d (in eV) for InxGa1-xAs with

x=0 025 050 053 075 and 10 Note that aX is the deformation potential exactly at the X-point ie not

at the X-valley minimum aX =aX for xgt025

ΞdΓ - aV ΞdX - aV ΞuX ΞdX - aV ΞuX ΞdL - aV ΞuL aVLDA

GaAs -854 -135 822 (861) -034 630 -838 151 (1426) 116

In025Ga075As -762 -025 709 -025 709 -764 138 112

In05Ga05As -689 -023 615 -023 615 -715 130 108

In053Ga047As -681 -022 515 -022 515 -709 129 (1135) 108

In075Ga025As -634 -019 540 -019 540 -690 125 104

InAs -597 -016 483 (450) -016 483 -689 125 100

bw (eV) -147 - - -010 150 -196 338 0

Table 5 Hydrostatic and shear deformation potentials of the InxGa1-xAs compounds (x=0 025 050 053

075 and 10) calculated using the HSE06 functional for the conduction band valleys ΞdΓ - aV ΞdX - aV

ΞuX ΞdL - aV and ΞuL in units of eV where aV is the hydrostatic deformation potential for the average of

three top valence bands at the Γ- point bw is the compositional bowing parameter In the parenthesis and

last column we give the theoretical values of deformation potentials ΞuLDA and aVLDA which were obtained

using the DFT-LDA calculations for the binary alloys (GaAs and InAs) by Chris Van de Walle [Phys Rev B 39 1871 (1989)] Note that Vegards law is used to estimate the value of aV for the InxGa1-xAs ternary

alloys and ΞuΓ = 0 The strain effect on the electron and hole effective masses can be quantified in general within the kmiddotp model using the hydrostatic and shear deformation potentials (given in Table 4 and 5) as well as other material parameters calculated in Task 22 and tabulated in this report of D24

4 Mechanical properties of InxGa1-xAs alloys In Table 6 we summarize all the parameter values for mechanical properties such as elastic constants bulk modulus and Poisson ratios for the InxGa1-xAs ternary alloy with alloy composition x=0 05 and 10 The compositional bowing parameter (bw) values are also included in Table 6

Table 6 (below) Elastic constants bulk modulus and Poisson ratios calculated with LDA and hybrid functional (HSE) for the GaAs and InAs binary alloys as well as the InxGa1-xAs ternary alloy with alloy composition x=05 and 053 bw is the compositional bowing parameter for elastic constants In parentheses we give elastic constants calculated for x=053 using the bowing parameters bw reported in the table The experimental data are available for the GaAs and InAs binary alloys only see the publically available data at wwwiofferssiruSVANSMSemicondGaInAsindexhtml and the ldquoexperimentalrdquo data for the ternary alloy are reported assuming the bwexp=0

7

GaAs LDA HSE Experiment

C11 (GPa) 1168 1175 1190

C12 (GPa) 535 500 534

C44 (GPa) 584 603 596

B C (GPa) 746 316 725 338 753 328

ν [100][111] 031 0189 030 0174 031 0189

In05Ga05As LDA (x=053) bw LDA HSE (x=053) bw HSE ldquoExperimentrdquo (bw=0)

C11 (GPa) 964 (950) 184 974 (965) 155 1012

C12 (GPa) 501 (500) 34 466 (469) 22 494

C44 (GPa) 449 (440) 135 471 (452) 179 496

B C (GPa) 655 231 - 655 269 - 662 259

ν [100][111] 034 022 - 032 020 - 033 020

InAs LDA HSE Experiment

C11 (GPa) 843 852 834

C12 (GPa) 485 452 454

C44 (GPa) 376 403 395

B C (GPa) 604 179 585 200 581 190

ν [100][111] 036 024 035 022 035 022

5 Ab-initio derived tight-binding parameters as used in OMEN Based on the DFT data provided in Tables 2 and 3 tight-binding parameters were derived for GaAs and InAs in the nearest-neighbour sp3d5s basis with spin-orbit coupling A matlab code has been developed for that purpose that takes the calculated targets as a reference and adjusts 31 tight-binding parameters per material to best reproduce the DFT inputs As fitting algorithm a least square optimizer was used The results can be found in Table 7 while the comparison with the target values are provided in Table 8

Parameter Name GaAs InAs

Esa -55672 -59718

Epa 40861 35133

Esa 196445 178304

Eda 129739 121476

λa 01865 02086

Esc -03150 04069

Epc 66509 62861

Esc 225962 177002

Edc 126835 124012

λc 00238 00208

Vssσ -16407 -14971

Vssσ -37006 -39375

Vsascσ -13151 -11761

Vscsaσ -22119 -21139

8

Vsapcσ 26669 23960

Vscpaσ 29432 27722

Vsapcσ 18855 25972

Vscpaσ 10309 20772

Vsadcσ -26059 -25146

Vscdaσ -23376 -25469

Vsadcσ -06276 -08171

Vscdaσ -01321 -06311

Vppσ 41434 43422

Vppπ -14332 -13914

Vpadcσ -18447 -20641

Vpcdaσ -18843 -21072

Vpadcπ 25303 15239

Vpcdaπ 25086 18110

Vddσ -12696 -09595

Vddπ 25183 24508

Vppδ -08504 -14849 Table 7 List of the newly generated nearest-neighbour tight-binding parameters of GaAs and InAs in the

sp3d5s basis with spin-orbit coupling

Quantity GaAs (DFT) GaAs (TB) InAs (DFT) InAs (TB)

Egap(eV) 132 13219 039 03896

EVmax (eV) 00 00 00 00

EL (eV) 165 16481 153 15299

EX (eV) 191 19115 20 1999

Δso (eV) 036 03565 038 038

kxmin (2π) 086 087 10 10

me 0062 00617 0024 00232

mXt 021 01737 0237 02574

mXl 11 10141 17 17025

mLt 0106 00958 0114 01127

mLl 162 17362 191 19078

mhh [001] 0313 03682 0346 02678

mlh [001] 0078 0077 0029 00282

mhh [110] 0565 06418 0526 04941

mlh [110] 007 00706 0028 00269

mhh [111] 0772 08215 0636 06712

mlh [111] 007 0069 0028 00265

mso 016 01572 0106 00903 Table 8 Comparison between the DFT targets in Tables 2 and 3 and the results obtained with the nearest-

neighbour tight-binding parameters of Table 7

As a next step to be included in deliverable 25 the targets will be refined by applying a scissor operator to the DFT results so that the band gaps of GaAs and InAs at the Γ point exactly correspond to the experimentally determined values Once this is done tight-binding bowing parameters will be determined as in Ref 1 to be able to match any In composition in InxGa1-xAs ternary compounds within the virtual crystal approximation

1 M Luisier and G Klimeck ldquoInvestigation of InxGa1-xAs Ultra-Thin-Body Tunneling FETs using a Full-Band and Atomistic Approachrdquo International Conference on Simulation of Semiconductor Processes and Devices SISPAD 2009 San Diego CA USA September 2009

9

6 Band offsets Band offset values (obtained by hybrid functional calculations) for the relevant In05Ga05As|InP(001) interface as well as many other semiconductor interfaces are tabulated by Wadehra et al in their contribution published in Applied Physics Letters 97 092119 (2010)

7 Temperature and doping dependencies The temperature and doping dependences of the band structure parameters of the InxGa1-xAs ternary alloy can be found in the publically available database wwwiofferssiruSVANSMSemicondGaInAsindexhtml

8 Mechanical properties of III-Nitrides In this section we present the DFT-based data for the elastic constants of wurtzite and zincblende III-Nitrides GaN InN and AlN Also the calculated internal strain parameters are given The data is compared with available experimental data The following sections (9 to 12) then present further parameters related to III-N materials

81 Wurtzite InN GaN and AlN

Table 9 summarizes the elastic constants Cij for wurtzite InN GaN and AlN along with the five internal strain parameters ς1 ς2 ς3 ς4 and ς5 All of our calculations have been performed within the HSE scheme using the projector augmented-wave (PAW) method as implemented in the plane-wave-based ab initio package VASP Here the screening parameter μ was fixed to 02 and the mixing parameter α to 025 (which correspond to the HSE06 functional) the energy cutoff for plane waves was 600 eV the semicore d electrons of In and Ga were treated as valence electrons and a Γ-centred 6x6x4 k-point grid was used Where available experimental reference data is given

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

C11 (GPa) 2338 225 3686 390 4102 396

C12 (GPa) 1100 109 1316 145 1424 137

C13 (GPa) 916 108 957 106 1101 108

C33 (GPa) 2383 265 4062 398 3850 373

C44 (GPa) 554 55 1017 105 1229 116

ς1 0193 na 0156 na 0138 na

ς2 0107 na 0083 na 0086 na

ς3 0218 na 0159 na 0191 na

ς4 0337 na 0201 na 0199 na

ς5 0107 na 0141 na 0143 na

Table 9 Elastic constants Cij calculated within HSE06-DFT for wurtzite InN GaN and AlN along with the internal strain parameters ςi The experimental data for AlN and GaN have been taken from A Polian et al J Appl Phys 79 3343 (1996) while for InN the data is from J Serrano et al Phys Rev Lett 106

205501 (2011)

8

Vsapcσ 26669 23960

Vscpaσ 29432 27722

Vsapcσ 18855 25972

Vscpaσ 10309 20772

Vsadcσ -26059 -25146

Vscdaσ -23376 -25469

Vsadcσ -06276 -08171

Vscdaσ -01321 -06311

Vppσ 41434 43422

Vppπ -14332 -13914

Vpadcσ -18447 -20641

Vpcdaσ -18843 -21072

Vpadcπ 25303 15239

Vpcdaπ 25086 18110

Vddσ -12696 -09595

Vddπ 25183 24508

Vppδ -08504 -14849 Table 7 List of the newly generated nearest-neighbour tight-binding parameters of GaAs and InAs in the

sp3d5s basis with spin-orbit coupling

Quantity GaAs (DFT) GaAs (TB) InAs (DFT) InAs (TB)

Egap(eV) 132 13219 039 03896

EVmax (eV) 00 00 00 00

EL (eV) 165 16481 153 15299

EX (eV) 191 19115 20 1999

Δso (eV) 036 03565 038 038

kxmin (2π) 086 087 10 10

me 0062 00617 0024 00232

mXt 021 01737 0237 02574

mXl 11 10141 17 17025

mLt 0106 00958 0114 01127

mLl 162 17362 191 19078

mhh [001] 0313 03682 0346 02678

mlh [001] 0078 0077 0029 00282

mhh [110] 0565 06418 0526 04941

mlh [110] 007 00706 0028 00269

mhh [111] 0772 08215 0636 06712

mlh [111] 007 0069 0028 00265

mso 016 01572 0106 00903 Table 8 Comparison between the DFT targets in Tables 2 and 3 and the results obtained with the nearest-

neighbour tight-binding parameters of Table 7

As a next step to be included in deliverable 25 the targets will be refined by applying a scissor operator to the DFT results so that the band gaps of GaAs and InAs at the Γ point exactly correspond to the experimentally determined values Once this is done tight-binding bowing parameters will be determined as in Ref 1 to be able to match any In composition in InxGa1-xAs ternary compounds within the virtual crystal approximation

1 M Luisier and G Klimeck ldquoInvestigation of InxGa1-xAs Ultra-Thin-Body Tunneling FETs using a Full-Band and Atomistic Approachrdquo International Conference on Simulation of Semiconductor Processes and Devices SISPAD 2009 San Diego CA USA September 2009

9

6 Band offsets Band offset values (obtained by hybrid functional calculations) for the relevant In05Ga05As|InP(001) interface as well as many other semiconductor interfaces are tabulated by Wadehra et al in their contribution published in Applied Physics Letters 97 092119 (2010)

7 Temperature and doping dependencies The temperature and doping dependences of the band structure parameters of the InxGa1-xAs ternary alloy can be found in the publically available database wwwiofferssiruSVANSMSemicondGaInAsindexhtml

8 Mechanical properties of III-Nitrides In this section we present the DFT-based data for the elastic constants of wurtzite and zincblende III-Nitrides GaN InN and AlN Also the calculated internal strain parameters are given The data is compared with available experimental data The following sections (9 to 12) then present further parameters related to III-N materials

81 Wurtzite InN GaN and AlN

Table 9 summarizes the elastic constants Cij for wurtzite InN GaN and AlN along with the five internal strain parameters ς1 ς2 ς3 ς4 and ς5 All of our calculations have been performed within the HSE scheme using the projector augmented-wave (PAW) method as implemented in the plane-wave-based ab initio package VASP Here the screening parameter μ was fixed to 02 and the mixing parameter α to 025 (which correspond to the HSE06 functional) the energy cutoff for plane waves was 600 eV the semicore d electrons of In and Ga were treated as valence electrons and a Γ-centred 6x6x4 k-point grid was used Where available experimental reference data is given

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

C11 (GPa) 2338 225 3686 390 4102 396

C12 (GPa) 1100 109 1316 145 1424 137

C13 (GPa) 916 108 957 106 1101 108

C33 (GPa) 2383 265 4062 398 3850 373

C44 (GPa) 554 55 1017 105 1229 116

ς1 0193 na 0156 na 0138 na

ς2 0107 na 0083 na 0086 na

ς3 0218 na 0159 na 0191 na

ς4 0337 na 0201 na 0199 na

ς5 0107 na 0141 na 0143 na

Table 9 Elastic constants Cij calculated within HSE06-DFT for wurtzite InN GaN and AlN along with the internal strain parameters ςi The experimental data for AlN and GaN have been taken from A Polian et al J Appl Phys 79 3343 (1996) while for InN the data is from J Serrano et al Phys Rev Lett 106

205501 (2011)

9

6 Band offsets Band offset values (obtained by hybrid functional calculations) for the relevant In05Ga05As|InP(001) interface as well as many other semiconductor interfaces are tabulated by Wadehra et al in their contribution published in Applied Physics Letters 97 092119 (2010)

7 Temperature and doping dependencies The temperature and doping dependences of the band structure parameters of the InxGa1-xAs ternary alloy can be found in the publically available database wwwiofferssiruSVANSMSemicondGaInAsindexhtml

8 Mechanical properties of III-Nitrides In this section we present the DFT-based data for the elastic constants of wurtzite and zincblende III-Nitrides GaN InN and AlN Also the calculated internal strain parameters are given The data is compared with available experimental data The following sections (9 to 12) then present further parameters related to III-N materials

81 Wurtzite InN GaN and AlN

Table 9 summarizes the elastic constants Cij for wurtzite InN GaN and AlN along with the five internal strain parameters ς1 ς2 ς3 ς4 and ς5 All of our calculations have been performed within the HSE scheme using the projector augmented-wave (PAW) method as implemented in the plane-wave-based ab initio package VASP Here the screening parameter μ was fixed to 02 and the mixing parameter α to 025 (which correspond to the HSE06 functional) the energy cutoff for plane waves was 600 eV the semicore d electrons of In and Ga were treated as valence electrons and a Γ-centred 6x6x4 k-point grid was used Where available experimental reference data is given

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

C11 (GPa) 2338 225 3686 390 4102 396

C12 (GPa) 1100 109 1316 145 1424 137

C13 (GPa) 916 108 957 106 1101 108

C33 (GPa) 2383 265 4062 398 3850 373

C44 (GPa) 554 55 1017 105 1229 116

ς1 0193 na 0156 na 0138 na

ς2 0107 na 0083 na 0086 na

ς3 0218 na 0159 na 0191 na

ς4 0337 na 0201 na 0199 na

ς5 0107 na 0141 na 0143 na

Table 9 Elastic constants Cij calculated within HSE06-DFT for wurtzite InN GaN and AlN along with the internal strain parameters ςi The experimental data for AlN and GaN have been taken from A Polian et al J Appl Phys 79 3343 (1996) while for InN the data is from J Serrano et al Phys Rev Lett 106

205501 (2011)

10

82 Zincblende InN GaN and AlN

In Table 10 we report the hybrid (HSE06) functional calculated elastic constants Cij for zincblende InN GaN and AlN Additionally we also give the internal strain parameter (Kleinmann parameter) In the case of zincblende nitrides a similar scheme as in Sec 81 is used with a Γ-centered 6x6x6 k-point grid accounting for the cubic symmetry of the crystal but with the same settings otherwise Where available experimental data is given for comparison

InN GaN AlN

InN HSE Experiment HSE Experiment HSE Experiment

C11 (GPa) 1832 na 2886 285 3089 na

C12 (GPa) 1192 na 1541 na 1665 na

C44 (GPa) 915 na 1660 na 1960 na

ς 076 na 058 na 0545 na

Table 10 Elastic constants calculated within HSE06-DFT for zincblende InN GaN and AlN along with

the internal strain parameter ς The experimental data for GaN has been taken from D Moss et al J Phys D Appl Phys 42 115412 (2009)

9 Band offsets band gap and edge bowing parameters for III-Nitrides

In this section we report on the band gap and band edge bowing parameters for wurtzite InGaN AlGaN and AlInN alloys These calculations have been performed on the basis of the tight-binding model developed in Task 23 and have been benchmarked against experimental data The derived tight-binding parameters are reported in Sec 101 The calculation of band gap and band edge bowing parameters in the framework of HSE-DFT is difficult for the following reason Even though HSE-DFT band gaps overcome the band gap problem of LDA-DFT in general the HSE06 functionals might still underestimated the band gap in comparison to experimental data for certain materials This is for example the case for AlN and GaN while for InN HSE06 gives good agreement with experimental data as already highlighted in the literature (cf P G Moses et al J Chem Phys 134 084703 (2011)) Even though the band gaps can be corrected in the HSE scheme by adjusting the exact exchange mixing parameter α the mixing parameter then turns be different for AlN (αasymp35) GaN (αasymp28) and InN (α=25) This is obviously a problem when studying the band gap baviour over the full composition range of Al containing alloys Thus we decided here to use our developed tight-binding model to perform these calculations The benchmarking of the presented results against experimental data and literature HSE06-DFT data (P G Moses et al J Chem Phys 134 084703 (2011)) has been described in D23 in detail Here we summarize our results in Tables 11 12 and 13 While AlGaN behaves almost like a ldquoconventionalrdquo III-V alloy where the band gap bowing can be described by a single composition independent bowing parameter we find that in AlInN the band gap bowing parameter is strongly composition dependent The alloy InGaN represents an intermediate situation The band offsets for these calculations have been taken from literature HSE06-DFT data (P G Moses et al J Chem Phys 134 084703 (2011))

11

AlInN 5 8 10 13 15 18 25 35 50 65 75 85

bcb

(eV) 1401 106 929 767 701 623 495 392 308 254 222 196

bvb

(eV) -580 -468 -459 -407 -371 -368 -317 -251 -207 -198

-201 -192

b (eV) 1981 1535 1389 1174 1072 991 812 643 515 452 424

387

Table 11 Al1minusx InxN composition dependent bowing parameters for band gap [b] conduction [bCB] and

valence band [bVB] as a function of the In content x

InGaN 5 10 15 25 35 50 65 75 85

bcb (eV) 174 156 143 126 113 092 085 081 078

bvb (eV) minus103 minus104 minus099 minus102 minus100 minus102 minus097

minus097 minus104

b(x) 277 26 242 228 213 194 182 178 182

Table 12 Band-gap b and band edge (conduction band bcb valence band bvb) bowing parameters of InxGa1minusxN as a function of the In content x

AlGaN

bcb (eV) 078

bvb (eV) minus016

b (eV) 094

Table 13 Band-gap b and band edge (conduction band bcb valence band bvb) bowing parameters of

AlGaN

10 Ab-inito derived tight-binding parameters for III-Nitrides In this section we present the tight-binding parameters derived from HSE06-DFT bandstructures for wurtzite InN GaN and AlN

In Table 14 we report the tight-binding parameters for wurtzite InN GaN and AlN for an sp3 tight-binding model Please note that as discussed above even though HSE06-DFT overcomes the band gap problem of LDA for InN it still underestimates the band gaps of GaN and AlN Thus to derive tight-binding parameters that can be used for comparison with experiments in WP6 we have fitted the tight-binding parameters to the HSE06 band structures and adjusted then the cation s-orbital on-site energies E(sc) to match the experimental band gaps The fits to the original band structures have already been presented and discussed in D23 We note here also that when changing the exact exchange mixing parameter α the valence band structure was

12

changed leading for instance to smaller crystal field splitting energies in comparison with the experiment Therefore for a consistent picture we have performed all HSE-DFT calculations on the basis of the HSE06 functionals and adjusted then the tight-binding parameters as described above This gave very good results in terms of the band gap variation as a function of the composition as presented in D23

Parameter Name InN GaN AlN

E(sa) minus1192 minus1062 -102

E(pa) 049 082 066

E(pza) 046 079 092

E(sc) 048 091 206

E(pc) 653 668 1108

V(ss) minus161 minus597 -811

V(xx) 179 234 320

V(xy) 483 547 563

V(sapc) 189 409 304

V(pasc) 614 867 1031 Table 14 Tight-binding parameters (in eV) for the nearest neighbour sp3 model of wurtzite InN GaN and AlN

11 kp parameters for III-N materials In addition to wurtzite tight-binding parameters we have also extracted 8-band kp parameters for cubic nitrides This data is summarized in Table 16 We will also be extending the kp database further for the final release

Parameter Name InN GaN AlN

Ep 112502 90000 159000

me 00490 02659 03355

γ1 73290 22525 14302

γ2 30874 05280 03587

γ3 34165 08798 06240

Table 15 8-band kp parameters γ1γ2γ3me and Ep for zincblende InN GaN and AlN

12 Piezoelectric coefficients for III-V materials The aim of Task 23 was also to extract piezoelectric coefficients via Berry-Phase calculations from VASP within the HSE06 scheme These parameters are required for the modelling of nitride-based heterostructures targeted in WP6 Therefore we summarize here the outcome of our Berry-Phase HSE06 calculations In Sec 121 we address wurtzite InN GaN and AlN parameters while Sec 122 focuses on zincblende III-V materials in general

121 Wurtzite InN GaN and AlN

In Table 17 we report the hybrid (HSE06) functional calculated first-order piezoelectric coefficients of wurtzite InN GaN and AlN Additionally we present spontaneous polarization and Born effective charges For comparison available experimental data are given in the table

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

e15 (Cm2) minus042 na minus032 minus036 minus039 -048

e31 (Cm2) minus058 -055 minus044 minus041 minus063 -06

13

e33 (Cm2) 107 095 074 086 146 15

Pspon (Cm2) minus0049 na minus0040 na minus0091 na

Ζ1=Ζ2 285 na 264 na 253 na

Ζ3 302 na 277 na 268 na

Table 16 First-order piezoelectric coefficients e15 e31 and e33 for wurtzite InN GaN and AlN from HSE06-DFT Berry-Phase calculations Additionally the extracted spontaneous polarization Pspon and the Born effective charges Z1 Z2 and Z3 are given Experimental data on GaN piezoelectric coefficients eij is taken from P Witczak et al Semicond Sci Technol 30 035008 (2015) For InN the experimental data has been taken from A Hangleiter et al Appl Phys Lett 83 1169 (2003) while for AlN it has been taken from K Tsubouchi and N Mikoshiba IEEE Trans Sonics Ultrason SU-32 634 (1985)

122 Zincblende III-V materials

Table 18 summarizes first- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients derived from Berry-Phase HSE06-DFT calculations for zincblende III-V semiconductors

e14 (Cm2) B114 (Cm2) B124 (Cm2) B156 (Cm2)

AlN 0548 minus681 minus504 minus415

GaN 0366 minus538 minus673 minus318

InN 0593 minus596 minus632 minus200

AlP 0014 minus202 minus276 minus143

GaP minus0121 minus123 minus327 minus138

InP 0016 minus154 minus362 minus102

AlAs minus0055 minus161 minus259 minus132

GaAs minus0205 minus099 minus321 minus128

InAs minus0111 minus117 minus431 minus046

AlSb minus0094 minus076 minus199 minus082

GaSb minus0216 minus031 minus277 minus070

InSb minus0161 minus062 minus404 minus016

Table 17 First- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients for zincblende III-V semiconductor materials The data has been extracted from Berry-Phase calculations within the HSE06 scheme

13 Conclusions In conclusion we summarize the work presented in deliverable D24 ldquoInitial tight-binding and EMA parameter databaserdquo as follows

- Ab-initio band structures and material parameters (calculated in Tasks 22 and 23) as well as tight-binding model parameters (calculated in Tasks 24 and 25) used in OMEN and WP6 have been extracted and tabulated for the deliverable D24 A list of the corresponding parameters is bieng made publicly available on the DEEPEN website

- Scripts used for the extraction of material parameters such as band structures energies effective masses are also being made publicly available at the DEEPEN website

11

AlInN 5 8 10 13 15 18 25 35 50 65 75 85

bcb

(eV) 1401 106 929 767 701 623 495 392 308 254 222 196

bvb

(eV) -580 -468 -459 -407 -371 -368 -317 -251 -207 -198

-201 -192

b (eV) 1981 1535 1389 1174 1072 991 812 643 515 452 424

387

Table 11 Al1minusx InxN composition dependent bowing parameters for band gap [b] conduction [bCB] and

valence band [bVB] as a function of the In content x

InGaN 5 10 15 25 35 50 65 75 85

bcb (eV) 174 156 143 126 113 092 085 081 078

bvb (eV) minus103 minus104 minus099 minus102 minus100 minus102 minus097

minus097 minus104

b(x) 277 26 242 228 213 194 182 178 182

Table 12 Band-gap b and band edge (conduction band bcb valence band bvb) bowing parameters of InxGa1minusxN as a function of the In content x

AlGaN

bcb (eV) 078

bvb (eV) minus016

b (eV) 094

Table 13 Band-gap b and band edge (conduction band bcb valence band bvb) bowing parameters of

AlGaN

10 Ab-inito derived tight-binding parameters for III-Nitrides In this section we present the tight-binding parameters derived from HSE06-DFT bandstructures for wurtzite InN GaN and AlN

In Table 14 we report the tight-binding parameters for wurtzite InN GaN and AlN for an sp3 tight-binding model Please note that as discussed above even though HSE06-DFT overcomes the band gap problem of LDA for InN it still underestimates the band gaps of GaN and AlN Thus to derive tight-binding parameters that can be used for comparison with experiments in WP6 we have fitted the tight-binding parameters to the HSE06 band structures and adjusted then the cation s-orbital on-site energies E(sc) to match the experimental band gaps The fits to the original band structures have already been presented and discussed in D23 We note here also that when changing the exact exchange mixing parameter α the valence band structure was

12

changed leading for instance to smaller crystal field splitting energies in comparison with the experiment Therefore for a consistent picture we have performed all HSE-DFT calculations on the basis of the HSE06 functionals and adjusted then the tight-binding parameters as described above This gave very good results in terms of the band gap variation as a function of the composition as presented in D23

Parameter Name InN GaN AlN

E(sa) minus1192 minus1062 -102

E(pa) 049 082 066

E(pza) 046 079 092

E(sc) 048 091 206

E(pc) 653 668 1108

V(ss) minus161 minus597 -811

V(xx) 179 234 320

V(xy) 483 547 563

V(sapc) 189 409 304

V(pasc) 614 867 1031 Table 14 Tight-binding parameters (in eV) for the nearest neighbour sp3 model of wurtzite InN GaN and AlN

11 kp parameters for III-N materials In addition to wurtzite tight-binding parameters we have also extracted 8-band kp parameters for cubic nitrides This data is summarized in Table 16 We will also be extending the kp database further for the final release

Parameter Name InN GaN AlN

Ep 112502 90000 159000

me 00490 02659 03355

γ1 73290 22525 14302

γ2 30874 05280 03587

γ3 34165 08798 06240

Table 15 8-band kp parameters γ1γ2γ3me and Ep for zincblende InN GaN and AlN

12 Piezoelectric coefficients for III-V materials The aim of Task 23 was also to extract piezoelectric coefficients via Berry-Phase calculations from VASP within the HSE06 scheme These parameters are required for the modelling of nitride-based heterostructures targeted in WP6 Therefore we summarize here the outcome of our Berry-Phase HSE06 calculations In Sec 121 we address wurtzite InN GaN and AlN parameters while Sec 122 focuses on zincblende III-V materials in general

121 Wurtzite InN GaN and AlN

In Table 17 we report the hybrid (HSE06) functional calculated first-order piezoelectric coefficients of wurtzite InN GaN and AlN Additionally we present spontaneous polarization and Born effective charges For comparison available experimental data are given in the table

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

e15 (Cm2) minus042 na minus032 minus036 minus039 -048

e31 (Cm2) minus058 -055 minus044 minus041 minus063 -06

13

e33 (Cm2) 107 095 074 086 146 15

Pspon (Cm2) minus0049 na minus0040 na minus0091 na

Ζ1=Ζ2 285 na 264 na 253 na

Ζ3 302 na 277 na 268 na

Table 16 First-order piezoelectric coefficients e15 e31 and e33 for wurtzite InN GaN and AlN from HSE06-DFT Berry-Phase calculations Additionally the extracted spontaneous polarization Pspon and the Born effective charges Z1 Z2 and Z3 are given Experimental data on GaN piezoelectric coefficients eij is taken from P Witczak et al Semicond Sci Technol 30 035008 (2015) For InN the experimental data has been taken from A Hangleiter et al Appl Phys Lett 83 1169 (2003) while for AlN it has been taken from K Tsubouchi and N Mikoshiba IEEE Trans Sonics Ultrason SU-32 634 (1985)

122 Zincblende III-V materials

Table 18 summarizes first- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients derived from Berry-Phase HSE06-DFT calculations for zincblende III-V semiconductors

e14 (Cm2) B114 (Cm2) B124 (Cm2) B156 (Cm2)

AlN 0548 minus681 minus504 minus415

GaN 0366 minus538 minus673 minus318

InN 0593 minus596 minus632 minus200

AlP 0014 minus202 minus276 minus143

GaP minus0121 minus123 minus327 minus138

InP 0016 minus154 minus362 minus102

AlAs minus0055 minus161 minus259 minus132

GaAs minus0205 minus099 minus321 minus128

InAs minus0111 minus117 minus431 minus046

AlSb minus0094 minus076 minus199 minus082

GaSb minus0216 minus031 minus277 minus070

InSb minus0161 minus062 minus404 minus016

Table 17 First- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients for zincblende III-V semiconductor materials The data has been extracted from Berry-Phase calculations within the HSE06 scheme

13 Conclusions In conclusion we summarize the work presented in deliverable D24 ldquoInitial tight-binding and EMA parameter databaserdquo as follows

- Ab-initio band structures and material parameters (calculated in Tasks 22 and 23) as well as tight-binding model parameters (calculated in Tasks 24 and 25) used in OMEN and WP6 have been extracted and tabulated for the deliverable D24 A list of the corresponding parameters is bieng made publicly available on the DEEPEN website

- Scripts used for the extraction of material parameters such as band structures energies effective masses are also being made publicly available at the DEEPEN website

12

changed leading for instance to smaller crystal field splitting energies in comparison with the experiment Therefore for a consistent picture we have performed all HSE-DFT calculations on the basis of the HSE06 functionals and adjusted then the tight-binding parameters as described above This gave very good results in terms of the band gap variation as a function of the composition as presented in D23

Parameter Name InN GaN AlN

E(sa) minus1192 minus1062 -102

E(pa) 049 082 066

E(pza) 046 079 092

E(sc) 048 091 206

E(pc) 653 668 1108

V(ss) minus161 minus597 -811

V(xx) 179 234 320

V(xy) 483 547 563

V(sapc) 189 409 304

V(pasc) 614 867 1031 Table 14 Tight-binding parameters (in eV) for the nearest neighbour sp3 model of wurtzite InN GaN and AlN

11 kp parameters for III-N materials In addition to wurtzite tight-binding parameters we have also extracted 8-band kp parameters for cubic nitrides This data is summarized in Table 16 We will also be extending the kp database further for the final release

Parameter Name InN GaN AlN

Ep 112502 90000 159000

me 00490 02659 03355

γ1 73290 22525 14302

γ2 30874 05280 03587

γ3 34165 08798 06240

Table 15 8-band kp parameters γ1γ2γ3me and Ep for zincblende InN GaN and AlN

12 Piezoelectric coefficients for III-V materials The aim of Task 23 was also to extract piezoelectric coefficients via Berry-Phase calculations from VASP within the HSE06 scheme These parameters are required for the modelling of nitride-based heterostructures targeted in WP6 Therefore we summarize here the outcome of our Berry-Phase HSE06 calculations In Sec 121 we address wurtzite InN GaN and AlN parameters while Sec 122 focuses on zincblende III-V materials in general

121 Wurtzite InN GaN and AlN

In Table 17 we report the hybrid (HSE06) functional calculated first-order piezoelectric coefficients of wurtzite InN GaN and AlN Additionally we present spontaneous polarization and Born effective charges For comparison available experimental data are given in the table

InN GaN AlN

HSE Experiment HSE Experiment HSE Experiment

e15 (Cm2) minus042 na minus032 minus036 minus039 -048

e31 (Cm2) minus058 -055 minus044 minus041 minus063 -06

13

e33 (Cm2) 107 095 074 086 146 15

Pspon (Cm2) minus0049 na minus0040 na minus0091 na

Ζ1=Ζ2 285 na 264 na 253 na

Ζ3 302 na 277 na 268 na

Table 16 First-order piezoelectric coefficients e15 e31 and e33 for wurtzite InN GaN and AlN from HSE06-DFT Berry-Phase calculations Additionally the extracted spontaneous polarization Pspon and the Born effective charges Z1 Z2 and Z3 are given Experimental data on GaN piezoelectric coefficients eij is taken from P Witczak et al Semicond Sci Technol 30 035008 (2015) For InN the experimental data has been taken from A Hangleiter et al Appl Phys Lett 83 1169 (2003) while for AlN it has been taken from K Tsubouchi and N Mikoshiba IEEE Trans Sonics Ultrason SU-32 634 (1985)

122 Zincblende III-V materials

Table 18 summarizes first- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients derived from Berry-Phase HSE06-DFT calculations for zincblende III-V semiconductors

e14 (Cm2) B114 (Cm2) B124 (Cm2) B156 (Cm2)

AlN 0548 minus681 minus504 minus415

GaN 0366 minus538 minus673 minus318

InN 0593 minus596 minus632 minus200

AlP 0014 minus202 minus276 minus143

GaP minus0121 minus123 minus327 minus138

InP 0016 minus154 minus362 minus102

AlAs minus0055 minus161 minus259 minus132

GaAs minus0205 minus099 minus321 minus128

InAs minus0111 minus117 minus431 minus046

AlSb minus0094 minus076 minus199 minus082

GaSb minus0216 minus031 minus277 minus070

InSb minus0161 minus062 minus404 minus016

Table 17 First- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients for zincblende III-V semiconductor materials The data has been extracted from Berry-Phase calculations within the HSE06 scheme

13 Conclusions In conclusion we summarize the work presented in deliverable D24 ldquoInitial tight-binding and EMA parameter databaserdquo as follows

- Ab-initio band structures and material parameters (calculated in Tasks 22 and 23) as well as tight-binding model parameters (calculated in Tasks 24 and 25) used in OMEN and WP6 have been extracted and tabulated for the deliverable D24 A list of the corresponding parameters is bieng made publicly available on the DEEPEN website

- Scripts used for the extraction of material parameters such as band structures energies effective masses are also being made publicly available at the DEEPEN website

13

e33 (Cm2) 107 095 074 086 146 15

Pspon (Cm2) minus0049 na minus0040 na minus0091 na

Ζ1=Ζ2 285 na 264 na 253 na

Ζ3 302 na 277 na 268 na

Table 16 First-order piezoelectric coefficients e15 e31 and e33 for wurtzite InN GaN and AlN from HSE06-DFT Berry-Phase calculations Additionally the extracted spontaneous polarization Pspon and the Born effective charges Z1 Z2 and Z3 are given Experimental data on GaN piezoelectric coefficients eij is taken from P Witczak et al Semicond Sci Technol 30 035008 (2015) For InN the experimental data has been taken from A Hangleiter et al Appl Phys Lett 83 1169 (2003) while for AlN it has been taken from K Tsubouchi and N Mikoshiba IEEE Trans Sonics Ultrason SU-32 634 (1985)

122 Zincblende III-V materials

Table 18 summarizes first- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients derived from Berry-Phase HSE06-DFT calculations for zincblende III-V semiconductors

e14 (Cm2) B114 (Cm2) B124 (Cm2) B156 (Cm2)

AlN 0548 minus681 minus504 minus415

GaN 0366 minus538 minus673 minus318

InN 0593 minus596 minus632 minus200

AlP 0014 minus202 minus276 minus143

GaP minus0121 minus123 minus327 minus138

InP 0016 minus154 minus362 minus102

AlAs minus0055 minus161 minus259 minus132

GaAs minus0205 minus099 minus321 minus128

InAs minus0111 minus117 minus431 minus046

AlSb minus0094 minus076 minus199 minus082

GaSb minus0216 minus031 minus277 minus070

InSb minus0161 minus062 minus404 minus016

Table 17 First- (e14) and second-order (B114 B124 and B156) piezoelectric coefficients for zincblende III-V semiconductor materials The data has been extracted from Berry-Phase calculations within the HSE06 scheme

13 Conclusions In conclusion we summarize the work presented in deliverable D24 ldquoInitial tight-binding and EMA parameter databaserdquo as follows

- Ab-initio band structures and material parameters (calculated in Tasks 22 and 23) as well as tight-binding model parameters (calculated in Tasks 24 and 25) used in OMEN and WP6 have been extracted and tabulated for the deliverable D24 A list of the corresponding parameters is bieng made publicly available on the DEEPEN website

- Scripts used for the extraction of material parameters such as band structures energies effective masses are also being made publicly available at the DEEPEN website